... are expressed by the polynomial chaos expansion whose coefficients are sequentially updated when observations are available. The probabilistic collocation method is employed to solve for the coefficients of the polynomial chaos expansion. The probabilistic collocation method is non-intrusive to the reservoir...

... to the EnKF in the sense that it estimates the correlations between the state variables from the Polynomial Chaos Expansion (PCE). The coefficients in the PCE are determined by the Probabilistic Collocation Method (PCM). In this paper, the PCKF method is applied to a synthetic reservoir model that mimics...

... methods, i.e. probabilistic collocation method (PCM) and Smolyak method are used to determine the coefficients of the polynomials expansions by solving for the fluid saturations and pressures at different collocation points via the original partial differential equations. This approach is non-intrusive...